Selmer groups for elliptic curves in ℤ l d -extensions of function fields of characteristic p

Andrea Bandini[1]; Ignazio Longhi[2]

  • [1] Università della Calabria Dipartimento di Matematica via P. Bucci - Cubo 30B 87036 Arcavacata di Rende (CS) (Italy)
  • [2] National Taiwan University Department of Mathematics N ∘  1 section 4 Roosevelt Road Taipei 106 (Taiwan)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 6, page 2301-2327
  • ISSN: 0373-0956

Abstract

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Let F be a function field of characteristic p > 0 , ℱ / F a ℤ l d -extension (for some prime l ≠ p ) and E / F a non-isotrivial elliptic curve. We study the behaviour of the r -parts of the Selmer groups ( r any prime) in the subextensions of ℱ via appropriate versions of Mazur’s Control Theorem. As a consequence we prove that the limit of the Selmer groups is a cofinitely generated (in some cases cotorsion) module over the Iwasawa algebra of ℱ / F .

How to cite

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Bandini, Andrea, and Longhi, Ignazio. "Selmer groups for elliptic curves in $\mathbb{Z}_l^d$-extensions of function fields of characteristic $p$." Annales de l’institut Fourier 59.6 (2009): 2301-2327. <http://eudml.org/doc/10455>.

@article{Bandini2009,
abstract = {Let $F$ be a function field of characteristic $p&gt;0$, $\mathcal\{F\}/F$ a $\mathbb\{Z\}_l^d$-extension (for some prime $l\ne p$) and $E/F$ a non-isotrivial elliptic curve. We study the behaviour of the $r$-parts of the Selmer groups ($r$ any prime) in the subextensions of $\mathcal\{F\}$ via appropriate versions of Mazur’s Control Theorem. As a consequence we prove that the limit of the Selmer groups is a cofinitely generated (in some cases cotorsion) module over the Iwasawa algebra of $\mathcal\{F\}/F$.},
affiliation = {Università della Calabria Dipartimento di Matematica via P. Bucci - Cubo 30B 87036 Arcavacata di Rende (CS) (Italy); National Taiwan University Department of Mathematics N ∘  1 section 4 Roosevelt Road Taipei 106 (Taiwan)},
author = {Bandini, Andrea, Longhi, Ignazio},
journal = {Annales de l’institut Fourier},
keywords = {Selmer groups; elliptic curves; function fields; Iwasawa theory},
language = {eng},
number = {6},
pages = {2301-2327},
publisher = {Association des Annales de l’institut Fourier},
title = {Selmer groups for elliptic curves in $\mathbb\{Z\}_l^d$-extensions of function fields of characteristic $p$},
url = {http://eudml.org/doc/10455},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Bandini, Andrea
AU - Longhi, Ignazio
TI - Selmer groups for elliptic curves in $\mathbb{Z}_l^d$-extensions of function fields of characteristic $p$
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 6
SP - 2301
EP - 2327
AB - Let $F$ be a function field of characteristic $p&gt;0$, $\mathcal{F}/F$ a $\mathbb{Z}_l^d$-extension (for some prime $l\ne p$) and $E/F$ a non-isotrivial elliptic curve. We study the behaviour of the $r$-parts of the Selmer groups ($r$ any prime) in the subextensions of $\mathcal{F}$ via appropriate versions of Mazur’s Control Theorem. As a consequence we prove that the limit of the Selmer groups is a cofinitely generated (in some cases cotorsion) module over the Iwasawa algebra of $\mathcal{F}/F$.
LA - eng
KW - Selmer groups; elliptic curves; function fields; Iwasawa theory
UR - http://eudml.org/doc/10455
ER -

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